Strongly consistent marching schemes for the wave equation

Jing-Rebecca Li 1 Leslie Greengard
1 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : In this paper, we consider a class of explicit marching schemes first proposed in [1] for solving the wave equation in complex geometry using an embedded Cartesian grid. These schemes rely on an integral evolution formula for which the numerical domain of dependence adjusts automatically to contain the true domain of dependence. Here, we refine and analyze a subclass of such schemes, which satisfy a condition we refer to as strong u-consistency. This requires that the evolution scheme be exact for a single-valued approximation to the solution at the previous time steps. We provide evidence that many of these strongly u-consistent schemes are stable and converge at very high order even in the presence of small cells in the grid, while taking time steps dictated by the uniform grid spacing.
Type de document :
Article dans une revue
Journal of Computational Physics, Elsevier, 2003, 188 (1), pp.194--208
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https://hal.inria.fr/hal-00781127
Contributeur : Jing-Rebecca Li <>
Soumis le : vendredi 25 janvier 2013 - 14:01:08
Dernière modification le : jeudi 9 février 2017 - 15:17:07

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  • HAL Id : hal-00781127, version 1

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Jing-Rebecca Li, Leslie Greengard. Strongly consistent marching schemes for the wave equation. Journal of Computational Physics, Elsevier, 2003, 188 (1), pp.194--208. 〈hal-00781127〉

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